### Inverse Functions

Let the function

and have a range

If the each

then this correspondence defines a certain function

called inverse with respect to given function

The sufficient condition for existence of an inverse is a strict monotony of the original function

If the function increases (decreases), then the inverse function is also decreases (increases).

Graph of the inverse function

*be defined as the set of***y=f(x)****X**and have a range

**Y.**If the each

*is the element of***y***there exists a single value of***Y***such that***x****f(x)=y.**then this correspondence defines a certain function

**x=g(y)**called inverse with respect to given function

**y=f(x).**The sufficient condition for existence of an inverse is a strict monotony of the original function

**y=f(x).**If the function increases (decreases), then the inverse function is also decreases (increases).

Graph of the inverse function

*coincides with that of the function***x=g(y)***if the independent variable is marked off along the***y=f(x)***. If the independent variable is laid off along the***y-axis***i.e. if the inverse function is written in the form***x-axis***, then the graph of the inverse function will be symmetric to that of the function***y=g(x)***with respect to the bisector of the first and third quadrant.***y=f(x)**